In this paper, we study the geodetic convexity of graphs, focusing on the problem of the
complexity of computing a minimum hull set of a graph in several graph classes. For any two …

In this paper, we prove several inapproximability results on the P 3-convexity and the
geodesic convexity in graphs. We prove that determining the P 3-hull number and the …

Inspired by a result of Carathéodory [Über den Variabilitätsbereich der Fourierschen
Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo 32 (1911) …

In this paper, we introduce a new convexity on graphs similar to the well known P 3-
convexity [R. Barbosa, E. Coelho, M. Dourado, D. Rautenbach, JL Szwarcfiter, A. Toman. On …

Let G be a finite, simple, and undirected graph and let S be a set of vertices of G. If every
vertex having two neighbors inside S is also in S, then S is P 3-convex. The P 3-convex hull …

We give linear and polynomial time algorithms for computing the hull number of distance-
hereditary and chordal graphs, respectively. The complexity of computing the hull number in …

We give linear and polynomial time algorithms for computing a minimum hull-set in distance-
hereditary and chordal graphs respectively. Prior to our result a polynomial time algorithm …

In this paper, we study the (geodesic) hull number of graphs. For any two vertices u, v∈ V of
a connected undirected graph G=(V, E), the closed interval I [u, v] of u and v is the set of …

This thesis focuses on the study of structural properties of graphs whose understanding
enables the design of efficient algorithms for solving optimization problems. We are …

A proper colouring of a graph is a function that assigns a colour to each vertex with the
restriction that adjacent vertices are assigned with distinct colours. Proper colourings are a …